文档介绍：John Snygg
A New Approach
to Differential Geometry
Using Clifford’s Geometric
Algebra
John Snygg
433 Prospect St.
East Orange, NJ 07017
******@
ISBN 978-0-8176-8282-8 e-ISBN 978-0-8176-8283-5
DOI -0-8176-8283-5
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2011940217
Mathematics Subject Classification (2010): 11E88, 15A66, 53-XX, 53-03
c Springer Science+Business Media, LLC 2012
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
connection with any form of information storage and retrieval, electronic adaptation, computer software,
or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are
not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject
to proprietary rights.
Printed on acid-free paper
Springer is part of Springer Science+Business Media
(.com)
To Pertti Lounesto
Preface
This book was written with the intention that it be used as a text for an undergraduate
course. The end result is not only suitable for an undergraduate course but also ideal
for a masters level course directed toward future high school math teachers. It is also
appropriate for anyone who wants to acquaint himself or herself with the usefulness
of Clifford algebra. In that context, instructors teaching . students may want to
use it as a source book.
Most introductory books on differential geometry are restricted to three dimen-
sions. I use the notation used by geometers in n-dimensions. Admittedly, most of
my examples are in three dimensions. However in Chap. 3, I